Least Common Multiple (LCM) of 60 and 93
The least common multiple (LCM) of 60 and 93 is 1860.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 60 and 93?
First, calculate the GCD of 60 and 93 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 93 = 0 remainder 60 |
| 2 | 93 ÷ 60 = 1 remainder 33 |
| 3 | 60 ÷ 33 = 1 remainder 27 |
| 4 | 33 ÷ 27 = 1 remainder 6 |
| 5 | 27 ÷ 6 = 4 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 120 | 6360 |
| 106 and 195 | 20670 |
| 11 and 133 | 1463 |
| 195 and 24 | 1560 |
| 69 and 122 | 8418 |